The Problem of Local Chaos and 4 Ways to Solve It

In mathematics and physics, there is an interesting problem:

Even when a certain trajectory of motion can be determined, on a small local segment of this trajectory, the state can be described as uncertain, a kind of chaos. And yet, the elements of this segment still follow the general trajectory.

Such situations can arise in many fields. For example, in logistics: the overall route is known, but how the situation unfolds along each small segment is unclear. And yet, somehow the route is completed.

We can look at this problem from four different perspectives, corresponding to the four types of intelligence. Let’s imagine it and model how each type would approach it.

We will approach this as a scenario where four types of intelligence encounter a problem, which, in the language of physics and mathematics, reflects:

• the presence of a defined general trajectory,

• local uncertainty, chaos, "fluctuation",

• yet each fragment still obeys an overarching law.

We will also use concepts such as factorial, integral, quantum, domain, dominant — as thinking tools for each type.

How the 4 types of intelligence might perceive this problem

✨ Intuitive Type (N)

How they react:

• Grasp the paradox of the whole and the part.

• See behind local chaos the "greater plan" of motion.

Words they choose:

• "Dominant force", "fields of probability", "potential structure", "unpredictability as part of a pattern".

How they explain:

"We see only local bursts of chaos, but at a deeper level, an invisible structure operates, a field of vectors guiding development.Just like a river is not afraid of eddies because it knows where it flows."

In a more expanded form:

"When I look at this trajectory, I feel that behind each tiny fluctuation lies an invisible web of meaning. There is no true disorder here. Even chaos is part of a larger plan. Like in the quantum world: particles seem to dance on the edge of uncertainty, yet their dance follows laws that remain unseen to the eye. It's as if the river, winding its way, always knew where it was destined to arrive .I don't want to break this system into pieces — I want to sense the entire trajectory, its spirit, its purpose. Local leaps are the breathing of a larger body, its life. We should not focus on the points but on the force that drives them."

Key metaphor:The deep "flow of fields of possibilities."

Thinking tool:The intuitive type would likely use the idea of quantum states and dominants, showing that small-scale uncertainty is a natural part of the greater picture.

✨ Logical Type (T)

How they react:

• Strive to formalize the behavior of the system.

• Search for mathematical tools to describe it.

Words they choose:

• "Integral", "gradient", "limit", "differentiation", "invariants".

How they explain:

"Over a small segment, behavior appears chaotic, but if we integrate across the whole trajectory, a regular pattern emerges.The integral sums local fluctuations into a general motion."

In a more expanded form:

"At first glance, the trajectory looks chaotic. But if we stop, break it down, map it — everything becomes explainable. Each local segment is a function of initial conditions plus environmental fluctuation. If I integrate behavior across a long enough interval, patterns will naturally reveal themselves. Chaos is merely a question of scale. Local uncertainty is compensated by the overall trend.We must find invariants: what remains unchanged despite transformations. It’s like an integral: by summing small unclear pieces, we obtain a clear direction."

Key metaphor:The integral as a victory over local instability.

Thinking tool:The logical type would instinctively turn to the integral — as a way to "absorb" chaos and reveal order at a larger scale.

✨ Ethical Type (F)

How they react:

• Feel the tension between order and chaos as an inner drama.

• See an analogy to the human journey.

Words they choose:

• "Potential", "possibilities", "integrity", "purpose", "emergence".

How they explain:

"Just like in life: sometimes our actions seem chaotic to us, but from a distance, they weave a deep, coherent path of becoming.The main thing is to keep the inner compass."

In a more expanded form:

"I see here the image of human life. We rush about, make decisions, make mistakes. Each separate action seems random, sometimes chaotic. But looking back after years — everything finds its meaning. Local uncertainty is a trial of freedom. It is in moments of chaos that new meanings and paths are born. What matters is not losing oneself. It’s vital to remember your inner compass, your center of gravity — otherwise, the trajectory may fall apart. The dominant of feeling, integrity, and love for a larger whole helps to pass through any uncertainty without fear."

Key metaphor: Human destiny as a great picture formed from fleeting moments.

Thinking tool:The ethical type intuitively uses dominants and fields of meaning, treating chaos as an expression of deep values and the emergence of wholeness.

✨ Sensorial Type (S)

How they react:

• Seek concrete manifestations of the trajectory in small segments.

• Want to see clear patterns firsthand.

Words they choose:

• "Functions", "steps", "discrete stages", "checkpoints".

How they explain:

"If we break the movement into small, clear stages, we’ll see that each local segment corresponds to a specific task. The main thing is to mark these points and adjust the direction accordingly."

In a more expanded form:

"I don’t need to grasp the entire flow at once.I look at what is happening here and now. Each segment of this trajectory is a concrete event, a specific step. Maybe the small segment looks messy, but if we mark control points — we’ll see a sequence. Like in a factorial: each step depends on the previous one, every result accumulates through concrete actions. It’s not necessary to see the whole river immediately. It's enough to know how to cross the nearest part, then the next. That's how a real, reliable path is built."

Key metaphor: Checkpoints as the foundation of stable movement.

Thinking tool:The sensorial type will naturally use the factorial — modeling the accumulation of discrete, sequential steps where every local moment matters.

✨ Summary

Type of Intelligence	Key Words	Thinking Tool	How They See the Problem
Intuitive (N)	Dominant force, potentials	Quantum states	Deep hidden order
Logical (T)	Integral, gradient	Integral thinking	Formalizing the whole via small changes
Ethical (F)	Integrity, meaning	Fields of meanings	Spiritual development through chaos
Sensorial (S)	Steps, checkpoints	Factorial, discretization	Seeing concrete steps along the path

Final phrase:

"Each type of intelligence perceives local uncertainty through the lens of its inner nature.Yet in the unified flow of time, like in the integral of a great journey, it is the combination of different styles of thinking that creates a living, true trajectory of development — both within an individual and within humanity as a whole."

Where Coherence is Applied

Coherence is a fundamental concept in many fields:

Field	Application of Coherence
Physics	Coherence of waves (laser light, quantum states)
Quantum Mechanics	Quantum coherence of particles in superposition
Engineering (Signal Processing)	Phase coherence of signals, stable transmission
Neuroscience	Neural coherence between different brain regions (brain waves)
Psychology and Cognitive Science	Coherent thinking, emotional coherence between thoughts and feelings
Organizational Theory	Coherence between departments, strategies, values
Education	Coherence of curriculum and learning paths

✨ Examples

1. In Physics (Optics and Lasers)

• Laser beams are highly coherent light sources:all photons have the same frequency, same phase, and move together.

Without coherence, light would scatter and blur; with coherence, it stays focused and powerful.

2. In Quantum Mechanics

• In quantum computing, quantum coherence is crucial:it allows qubits to exist in superposition states and interact meaningfully without immediate collapse.

• Decoherence happens when external noise destroys this delicate alignment.

3. In Neuroscience

• Neural coherence describes how brain regions synchronize their electrical activity.

• High coherence between the prefrontal cortex and limbic system, for example, is linked to emotional regulation and focused attention.

✨ Important Formulas

1. Degree of Coherence (First-Order Coherence)

In optics and quantum theory, the degree of coherence can be mathematically described by:

Meaning:

Quantum coherence is associated with off-diagonal elements of the density matrix ρ:

✨ Visual Example (Physics)

• Coherent light: all waves peak and trough together → powerful focused beam (like a laser).

• Incoherent light: peaks and troughs occur randomly → scattered, dim light (like a regular light bulb).

✨ Final Definition

"Coherence is the invisible thread that binds elements into a unified, structured, and meaningful whole — whether it's waves, thoughts, particles, or teams."